17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
Obs
visits
1
18573
2465673 4365
23460
1
2
100589
4523535 2920
24991
2 11.5188 15.3248 10.1263 7.97934 0.022237
3
11690
1404179 4043
21945
3
4 1456666 31985112 2397
32225
4 14.1917 17.2808 10.3805 7.78197 0.045542
5
110480
3633185 3346
32441
5 11.6126 15.1056 10.3872 8.11552 0.030409
6
27672
2988059 5022
40870
6 10.2282 14.9101 10.6182 8.52158 0.009261
7
6594
572059 4839
38374
7
8.7939 13.2570 10.5551 8.48446 0.011527
8
4948
627758 4854
31074
8
8.5067 13.3499 10.3441 8.48756 0.007882
87514 14270020 4717
27836
9 11.3796 16.4737 10.2341 8.45893 0.006133
10
62041
5864163 4499
27790 10 11.0356 15.5844 10.2324 8.41161 0.010580
11
23931
856962 2915
23640 11 10.0829 13.6611 10.0707 7.97763 0.027925
138588 10909520 4255
31842 12 11.8393 16.2051 10.3685 8.35585 0.012703
9
12
pop
dist income
id
lvisits
lpop lincome
LDist
p_visits
9.8295 14.7180 10.0631 8.38137 0.007533
9.3665 14.1550
9.9963 8.30474 0.008325
13
43346
4304011 4346
26838 13 10.6770 15.2751 10.1976 8.37701 0.010071
14
24544
1787432 3947
26376 14 10.1082 14.3963 10.1802 8.28071 0.013731
15
23869
1920669 3919
27408 15 10.0803 14.4682 10.2186 8.27359 0.012427
16
20993
2253800 4392
24057 16
9.9519 14.6281 10.0882 8.38754 0.009314
17
16750
3245665 4236
23041 17
9.7262 14.9928 10.0450 8.35137 0.005161
18
7159
512878 5120
25399 18
8.8761 13.1478 10.1425 8.54091 0.013958
19
47525
4558668 4854
33621 19 10.7690 15.3325 10.4229 8.48756 0.010425
20
55894
5801367 5096
37710 20 10.9312 15.5736 10.5377 8.53621 0.009635
21
88413
7419457 4488
29071 21 11.3898 15.8196 10.2775 8.40916 0.011916
22
84262
3490059 3981
31913 22 11.3417 15.0654 10.3708 8.28929 0.024143
23
8581
1387351 4189
20856 23
24
48170
3883442 4152
27186 24 10.7825 15.1722 10.2105 8.33135 0.012404
25
15019
487878 3059
22541 25
9.6171 13.0978 10.0231 8.02584 0.030784
26
14280
1193725 3826
27658 26
9.5666 13.9926 10.2277 8.24958 0.011963
27
55621
1828646 2791
29551 27 10.9263 14.4191 10.2939 7.93416 0.030416
28
8996
732335 5096
29
70559
7939087 4968
37112 29 11.1642 15.8873 10.5217 8.51077 0.008888
30
20509
1363501 3459
21883 30
31
117496 16602582 4968
33042 28
9.0573 14.1429
9.9454 8.34022 0.006185
9.1045 13.5040 10.4055 8.53621 0.012284
9.9286 14.1256
9.9935 8.14873 0.015041
34502 31 11.6742 16.6251 10.4488 8.51077 0.007077
32
40666
4849482 4682
26842 32 10.6131 15.3944 10.1977 8.45148 0.008386
33
5160
358958 3693
34
78393
8782329 4440
27914 34 11.2695 15.9883 10.2369 8.39841 0.008926
35
22838
2254563 3744
23582 35 10.0362 14.6285 10.0682 8.22791 0.010130
36
135883
2694144 2500
27649 36 11.8195 14.8066 10.2273 7.82405 0.050436
37
68920
9464101 4920
29533 37 11.1407 16.0630 10.2933 8.50106 0.007282
38
6407
953146 5085
29158 38
8.7651 13.7675 10.2805 8.53405 0.006722
39
16479
2427124 4686
23952 39
9.7098 14.7022 10.0838 8.45233 0.006790
24780 33
8.5487 12.7910 10.1178 8.21419 0.014375
1
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
Obs
visits
40
6182
391427 3630
41
30220
3620018 4166
25878 41 10.3163 15.1020 10.1611 8.33471 0.008348
177789 17204281 3937
27722 42 12.0884 16.6607 10.2300 8.27817 0.010334
42
pop
dist income
id
25993 40
lvisits
lpop lincome
LDist
p_visits
8.7294 12.8776 10.1656 8.19699 0.015793
43
58460
1970344 2997
23364 43 10.9761 14.4937 10.0590 8.00537 0.029670
44
4225
232448 4999
45
68202
5169955 4849
31065 45 11.1302 15.4584 10.3438 8.48653 0.013192
46
302474
4831106 2680
31129 46 12.6198 15.3906 10.3459 7.89357 0.062610
47
5541
832780 4602
48
54059
3663643 4239
49
6428
321344 3314
26904 44
21767 47
8.3488 12.3564 10.2000 8.51699 0.018176
8.6199 13.6325
9.9882 8.43425 0.006654
28066 48 10.8978 15.1140 10.2423 8.35208 0.014756
27436 49
8.7684 12.6803 10.2196 8.10591 0.020003
2
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
histograms
FREQUENCY
50
40
30
20
10
0
125000
375000
625000
875000
visits MIDPOINT
1125000
1375000
3
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
histograms
FREQUENCY
13
12
11
10
9
8
7
6
5
4
3
2
1
0
2500
3000
3500
4000
dist MIDPOINT
4500
5000
4
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
histograms
FREQUENCY
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
20000
24000
28000
32000
income MIDPOINT
36000
40000
5
17:38 Saturday, July 10, 2010
6
Visits to Hawaii from all 49 US States- year 2000
Scatter Plots
lvisits
15
14
13
12
11
10
9
8
7.7
7.8
7.9
8.0
8.1
8.2
LDist
8.3
8.4
8.5
8.6
17:38 Saturday, July 10, 2010
7
Visits to Hawaii from all 49 US States- year 2000
Scatter Plots
lvisits
15
14
13
12
11
10
9
8
9.9
10.0
10.1
10.2
10.3
lincome
10.4
10.5
10.6
10.7
17:38 Saturday, July 10, 2010
8
Visits to Hawaii from all 49 US States- year 2000
Scatter Plots
lvisits
15
14
13
12
11
10
9
8
12
13
14
15
lpop
16
17
18
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
1. Correlation analysis
The CORR Procedure
4 Variables: lvisits lincome lpop
LDist
Simple Statistics
Variable
N
Mean Std Dev
Sum Minimum Maximum
lvisits
49 10.37665 1.23460 508.45567
8.34877
14.19166
lincome
49 10.23242 0.15902 501.38836
9.94540
10.61815
lpop
49 14.72651 1.14216 721.59906 12.35642
17.28078
LDist
49
8.30591 0.20554 406.98962
7.78197
Pearson Correlation Coefficients, N = 49
Prob > |r| under H0: Rho=0
lvisits lincome
lpop
LDist
lvisits
1.00000 0.35395 0.88172 -0.37959
0.0126 <.0001
0.0071
lincome
0.35395 1.00000 0.34311
0.0126
0.0158
0.27147
0.0592
lpop
0.88172 0.34311 1.00000
<.0001 0.0158
0.01058
0.9425
LDist
-0.37959 0.27147 0.01058
0.0071 0.0592 0.9425
1.00000
8.54091
9
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
2. Model Lvisits = lpop
Natural log transformation
The REG Procedure
Model: MODEL1
Dependent Variable: lvisits
Number of Observations Read
49
Number of Observations Used
49
Analysis of Variance
Source
DF
Model
Sum of
Squares
Mean
Square F Value
1 56.87971 56.87971
Error
47 16.28324
Corrected Total
48 73.16295
Root MSE
164.18 <.0001
0.34645
0.58860 R-Square 0.7774
Dependent Mean 10.37665 Adj R-Sq
Coeff Var
Pr > F
0.7727
5.67237
Parameter Estimates
Variable DF
Parameter Standard
Estimate
Error t Value Pr > |t|
Type I SS Type II SS
Intercept
1
-3.65896
1.09863
-3.33 0.0017 5276.06475
lpop
1
0.95308
0.07438
12.81 <.0001
56.87971
3.84289
56.87971
10
17:38 Saturday, July 10, 2010
11
Visits to Hawaii from all 49 US States- year 2000
2. Model Lvisits = lpop
observed and predicted value
lvisits
15
14
13
12
11
10
9
8
12
13
14
15
16
lpop
PLOT
lvisits
Predicted Value of lvisits
17
18
17:38 Saturday, July 10, 2010
12
Visits to Hawaii from all 49 US States- year 2000
2. Model Lvisits = lpop
Residual plot
Residual
2
1
0
-1
8
9
10
11
Predicted Value of lvisits
12
13
17:38 Saturday, July 10, 2010
13
Visits to Hawaii from all 49 US States- year 2000
2. Model Lvisits = lpop
Residual plot
Residual
2
1
0
-1
9.9
10.0
10.1
10.2
10.3
lincome
10.4
10.5
10.6
10.7
17:38 Saturday, July 10, 2010
14
Visits to Hawaii from all 49 US States- year 2000
2. Model Lvisits = lpop
Residual plot
Residual
2
1
0
-1
7.7
7.8
7.9
8.0
8.1
8.2
LDist
8.3
8.4
8.5
8.6
17:38 Saturday, July 10, 2010
15
Visits to Hawaii from all 49 US States- year 2000
2. Model Lvisits = lpop
Residual plot
Residual
2
1
0
-1
12
13
14
15
lpop
16
17
18
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
3. Lvisits = lpop ldist lincome
log transformation
The REG Procedure
Model: MODEL1
Dependent Variable: lvisits
Number of Observations Read
49
Number of Observations Used
49
Analysis of Variance
Source
DF
Model
Sum of
Squares
Mean
Square F Value
3 70.13280 23.37760
Error
45
Corrected Total
48 73.16295
Root MSE
3.03015
347.18 <.0001
0.06734
0.25949 R-Square 0.9586
Dependent Mean 10.37665 Adj R-Sq
Coeff Var
Pr > F
0.9558
2.50074
Parameter Estimates
Variable DF
Parameter Standard
Estimate
Error t Value Pr > |t|
Type I SS Type II SS
Intercept
1
4.03531
2.58618
1.56 0.1257 5276.06475
0.16394
lpop
1
0.88692
0.03506
25.30 <.0001
56.87971
43.09538
LDist
1
-2.64516
0.19013
-13.91 <.0001
11.06757
13.03382
lincome
1
1.49042
0.26161
5.70 <.0001
2.18552
2.18552
16
17:38 Saturday, July 10, 2010
17
Visits to Hawaii from all 49 US States- year 2000
3. Lvisits = lpop ldist lincome
Residual plot
Residual
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
7
8
9
10
11
Predicted Value of lvisits
12
13
14
15
17:38 Saturday, July 10, 2010
18
Visits to Hawaii from all 49 US States- year 2000
3. Lvisits = lpop ldist lincome
Residual plot
Residual
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
9.9
10.0
10.1
10.2
10.3
lincome
10.4
10.5
10.6
10.7
17:38 Saturday, July 10, 2010
19
Visits to Hawaii from all 49 US States- year 2000
3. Lvisits = lpop ldist lincome
Residual plot
Residual
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
7.7
7.8
7.9
8.0
8.1
8.2
LDist
8.3
8.4
8.5
8.6
17:38 Saturday, July 10, 2010
20
Visits to Hawaii from all 49 US States- year 2000
3. Lvisits = lpop ldist lincome
Residual plot
Residual
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
12
13
14
15
lpop
16
17
18
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
3. Lvisits = lpop ldist lincome
histograms
FREQUENCY
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
-0.4
-0.2
0.0
0.2
Residual
0.4
0.6
21
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
3. Lvisits = lpop ldist lincome
Normality test - Resid
The CAPABILITY Procedure
Variable: Resid (Residual)
Moments
N
49 Sum Weights
Mean
49
0 Sum Observations
0
Std Deviation
0.25125292 Variance
0.06312803
Skewness
0.72500651 Kurtosis
0.54040311
Uncorrected SS 3.03014552 Corrected SS
3.03014552
Coeff Variation
0.03589327
. Std Error Mean
Basic Statistical Measures
Location
Mean
Variability
0.00000 Std Deviation
0.25125
Median -0.03645 Variance
0.06313
Mode
1.16798
. Range
Interquartile Range 0.29358
Tests for Location: Mu0=0
Test
Statistic
Student's t
t
Sign
M
p Value
0 Pr > |t|
1.0000
-0.5 Pr >= |M| 1.0000
Signed Rank S
-52.5 Pr >= |S|
0.6066
Tests for Normality
Test
Statistic
Shapiro-Wilk
p Value
W
0.960986 Pr < W
0.1040
Kolmogorov-Smirnov D
0.085098 Pr > D
>0.1500
Cramer-von Mises
W-Sq 0.068782 Pr > W-Sq >0.2500
Anderson-Darling
A-Sq
0.508756 Pr > A-Sq
Quantiles (Definition 5)
Quantile
Estimate
100% Max
0.6808222653
99%
0.6808222653
95%
0.4161759168
90%
0.3942895038
75% Q3
0.1105326049
50% Median -0.0364537204
25% Q1
-0.1830438476
0.1983
22
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
3. Lvisits = lpop ldist lincome
Normality test - Resid
The CAPABILITY Procedure
Variable: Resid (Residual)
Quantiles (Definition 5)
Quantile
Estimate
10%
-0.3010450735
5%
-0.3157472684
1%
-0.4871548182
0% Min
-0.4871548182
Extreme Observations
Lowest
Highest
Value Obs
Value Obs
-0.487154818
17 0.394289504
46
-0.334981506
8 0.414274360
22
-0.315747268
6 0.416175917
45
-0.303320679
49 0.655349710
18
-0.301045074
26 0.680822265
44
23
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
3. Lvisits = lpop ldist lincome
Normality test - Resid
35
30
25
Percent
20
15
10
5
0
-0.6
-0.4
-0.2
0
0.2
Residual
Curve:
Normal(Mu=0 Sigma=0.2513)
0.4
0.6
24
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
3. Lvisits = lpop ldist lincome
Normality test - Resid
The CAPABILITY Procedure
Fitted Normal Distribution for Resid
Parameters for Normal
Distribution
Parameter Symbol
Mean
Mu
Std Dev
Sigma
Estimate
0
0.251253
Goodness-of-Fit Tests for Normal Distribution
Test
Statistic
DF
p Value
Kolmogorov-Smirnov D
0.08509752
Pr > D
>0.150
Cramer-von Mises
W-Sq
0.06878222
Pr > W-Sq
>0.250
Anderson-Darling
A-Sq
0.50875586
Pr > A-Sq
0.198
Chi-Square
Chi-Sq 2.48763671
3 Pr > Chi-Sq
0.478
Quantiles for Normal
Distribution
Quantile
Percent Observed Estimated
1.0
-0.48715 -0.584502
5.0
-0.31575 -0.413274
10.0
-0.30105 -0.321994
25.0
-0.18304 -0.169468
50.0
-0.03645 -0.000000
75.0
0.11053
0.169468
90.0
0.39429
0.321994
95.0
0.41618
0.413274
99.0
0.68082
0.584502
25
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
4. lvisits on ldist and lincome and lpop plus interactions
natural log transformation
The GLM Procedure
Number of Observations Read
49
Number of Observations Used
49
26
17:38 Saturday, July 10, 2010
Visits to Hawaii from all 49 US States- year 2000
4. lvisits on ldist and lincome and lpop plus interactions
natural log transformation
The GLM Procedure
Dependent Variable: lvisits
Source
DF
Model
Sum of
Squares Mean Square F Value
6 70.32835421 11.72139237
Error
42
2.83459119
Corrected Total
48 73.16294540
Pr > F
173.68 <.0001
0.06749027
R-Square Coeff Var Root MSE lvisits Mean
0.961256 2.503592
Source
DF
0.259789
10.37665
Type I SS Mean Square F Value
Pr > F
lpop
1 56.87970931 56.87970931
842.78 <.0001
LDist
1 11.06757014 11.06757014
163.99 <.0001
lincome
1
2.18552043
2.18552043
32.38 <.0001
lpop*LDist
1
0.09002593
0.09002593
1.33 0.2546
lpop*lincome
1
0.08716311
0.08716311
1.29 0.2622
LDist*lincome
1
0.01836528
0.01836528
0.27 0.6047
Source
DF
Type III SS Mean Square F Value
Pr > F
lpop
1 0.01017115
0.01017115
0.15 0.6998
LDist
1 0.01868250
0.01868250
0.28 0.6016
lincome
1 0.00598728
0.00598728
0.09 0.7673
lpop*LDist
1 0.04030020
0.04030020
0.60 0.4440
lpop*lincome
1 0.08929023
0.08929023
1.32 0.2566
LDist*lincome
1 0.01836528
0.01836528
0.27 0.6047
Parameter
Intercept
Estimate
Standard
Error t Value Pr > |t|
-41.45996447 136.4434838
-0.30 0.7627
lpop
-1.14215036
2.9421093
-0.39 0.6998
LDist
8.31307603
15.8002811
0.53 0.6016
lincome
4.30065771
14.4391207
0.30 0.7673
-0.13292391
0.1720165
-0.77 0.4440
lpop*lincome
0.30460740
0.2648250
1.15 0.2566
LDist*lincome
-0.87128062
1.6702436
-0.52 0.6047
lpop*LDist
27